Weak passive table. I raise to $25 after a limper with [4s]. The BB is fairly loose and doesnt understand the basics of the game (position, trouble hands), but is good enough to beat the avg fish. He calls and we're heads up.

Pot $55. Flop [Qd][5d]. He quickly checks. I check behind.
Pot $55. Turn . he leads $40 and I call.
Pot $135. River . He checks.....my play?

NEXT TRAIN TO VALUETOWN!!!!

bet anywhere from 40-80 depending on how much you think he'll call.

Mjeh. Even though I think you have the best here often hand I see no point in betting.

I think your chance of having the bets hand if you check is high, but the chance of you having the best hand if you bet AND get called is too low for you to valuebet it.

I think you're good here most of the time. Whether to bet depends a lot on how you've been playing.

If you've made a few suspicious bets (and given that you are raising K4s, this seems possible), villian will pay you off here enough with hands like QT, AJ. If you've been TAGish mostly I'd check behind.

I bet because he can have lots of K's that beat you...you're betting on a bluff.